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Isometries of certain operator spaces
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Let
X
X
and
Y
Y
be Banach spaces, and
L
(
X
,
Y
)
L(X,Y)
be the spaces of bounded linear operators from
X
X
into
Y
.
Y.
In this paper we give full characterization of isometric onto operators of
L
(
X
,
Y
)
,
L(X,Y),
for a certain class of Banach spaces, that includes
ℓ
p
,
\ell ^{p},
1
>
p
>
∞
.
1>p>\infty .
We also characterize the isometric onto operators of
L
(
c
0
)
L(c_{0})
and
K
(
ℓ
1
)
,
K(\ell ^{1}),
the compact operators on
ℓ
1
.
\ell ^{1}.
Furthermore, the multiplicative isometric onto operators of
L
(
ℓ
1
)
L(\ell ^{1})
, when multiplication on
L
(
ℓ
1
)
L(\ell ^{1})
is taken to be the Schur product, are characterized.
American Mathematical Society (AMS)
Title: Isometries of certain operator spaces
Description:
Let
X
X
and
Y
Y
be Banach spaces, and
L
(
X
,
Y
)
L(X,Y)
be the spaces of bounded linear operators from
X
X
into
Y
.
Y.
In this paper we give full characterization of isometric onto operators of
L
(
X
,
Y
)
,
L(X,Y),
for a certain class of Banach spaces, that includes
ℓ
p
,
\ell ^{p},
1
>
p
>
∞
.
1>p>\infty .
We also characterize the isometric onto operators of
L
(
c
0
)
L(c_{0})
and
K
(
ℓ
1
)
,
K(\ell ^{1}),
the compact operators on
ℓ
1
.
\ell ^{1}.
Furthermore, the multiplicative isometric onto operators of
L
(
ℓ
1
)
L(\ell ^{1})
, when multiplication on
L
(
ℓ
1
)
L(\ell ^{1})
is taken to be the Schur product, are characterized.
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